a fruit seller sold 121 fruits in the morning and 1/4 of the remaining fruits in the afternoon. If he had 1/5 of the total number fruits left, how many fruits did he have at first?
+128474 OK.......
Call the total number of fruits started with, F
So......
After the seller sells 121 fruits... he has F - 121 reamaining
And he sells (1/ 4) of these in the afternoon =(1/4)(F - 121)
So.....what he/she strated with - what was sold in the morning - what was sold in the afternoon = (1/5)F
So....we have this equation
F - 121 - (1/4)(F - 121) = (1/5)F simplify
F - 121 - (1/4)F + 121/4 = (1/5)F
(3/4)F - 121 + 121/4 = (1/5)F
(3/4)F - 484/4 + 121/4 = (1/5)F
(3/4)F - 363/4 = (1/5)F subtract (1/5)F from both sides..add 363/4 to both sides
(3/4)F - (1/5)F = 363/4 get a common denominator on the right
(15/20) - (4/20) F = 363/4
(11/20)F = 363/4 multiply both sides by (20/11)
F = (363/4) (20/11) = (363/11) (20/4) = (33)(5) = 165 fruits
Proof
165 - 121 = 44 left after the morning
(1/4) of these sold in the afternoon = 11 sold and 33 remain......and this is (1/5) of the total
